Results 51 to 60 of about 1,094 (76)

Self-Similar Blowup Solutions to the 2-Component Degasperis-Procesi Shallow Water System

, 2010
In this article, we study the self-similar solutions of the 2-component Degasperis-Procesi water system:% [c]{c}% \rho_{t}+k_{2}u\rho_{x}+(k_{1}+k_{2})\rho u_{x}=0 u_{t}-u_{xxt}+4uu_{x}-3u_{x}u_{xx}-uu_{xxx}+k_{3}\rho\rho_{x}=0. By the separation method,
Camassa, Deng, Escher, Goldreich, Guan, Guo, Ivanov, Jin, Lakin, Li, Liu, Makino, Manwai Yuen, Popowicz, Yuen, Yuen, Yuen, Yuen, Yuen, Zhou   +19 more
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Analytical solutions of cylindrical and spherical dust ion-acoustic solitary waves

Results in Physics, 2019
In the present work, employing the conventional reductive perturbation method to the field equations of an unmagnetized dusty plasma consisting of inertial ions, Boltzmann electrons and stationary dust particles in the nonplanar geometry we derived ...
Essam. R. El-Zahar, Hilmi Demiray
doaj   +1 more source

Soliton equations: admitted solutions and invariances via B\"acklund transformations [PDF]

Open Communications in Nonlinear Mathematical Physics
A couple of applications of B\"acklund transformations in the study of nonlinear evolution equations is here given. Specifically, we are concerned about third order nonlinear evolution equations.
Sandra Carillo, Cornelia Schiebold
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Peaked solitary waves and shock waves of the Degasperis-Procesi-Kadomtsev-Petviashvili equation

Advances in Nonlinear Analysis
In this study, we establish the existence and nonexistence of smooth and peaked solitary wave solutions (or periodic) to the Degasperis-Procesi-Kadomtsev-Petviashvili (DP-KP) equation with a weak transverse effect.
Moon Byungsoo, Yang Chao
doaj   +1 more source

The initial-value problem for a Gardner-type equation

Advanced Nonlinear Studies
Discussed here is a regularized version(0.1)ut+ux+uux+Au2ux−uxxt=0, $${u}_{t}+{u}_{x}+u{u}_{x}+A{u}^{2}{u}_{x}-{u}_{\mathit{xxt}}=0,$$ of the classical Gardner equationut+ux+uux+Au2ux+uxxx=0, $${u}_{t}+{u}_{x}+u{u}_{x}+A{u}^{2}{u}_{x}+{u}_{\mathit{xxx ...
Bona Jerry, Chen Hongqiu, Guerrero Pamela, Haidau Cristina, Pantic Sanja   +4 more
doaj   +1 more source

Dissipative perturbations for the K(n,n) Rosenau-Hyman equation

, 2012
Compactons are compactly supported solitary waves for nondissipative evolution equations with nonlinear dispersion. In applications, these model equations are accompanied by dissipative terms which can be treated as small perturbations.
Abassy, Antonova, Bertozzi, Bin, Biswas, Biswas, Biswas, Cardenas, Cooper, Cooper, Cooper, de Frutos, Dey, Drazin, Ebadi, Fernandez, Francisco R. Villatoro, Johnson, Julio Garralón, Kardashov, Kevorkian, Khare, Kivshar, Kivshar, Kovalev, Laila, Lamb, Ludu, McLaughlin, Mihaila, Olver, Pikovsky, Rosenau, Rosenau, Rosenau, Rosenau, Rosenau, Rosenau, Rus, Rus, Rus, Rus, Triki, Zhang   +43 more
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Soliton surfaces associated with symmetries of ODEs written in Lax representation

, 2011
The main aim of this paper is to discuss recent results on the adaptation of the Fokas-Gel'fand procedure for constructing soliton surfaces in Lie algebras, which was originally derived for PDEs [Grundland, Post 2011], to the case of integrable ODEs ...
A M Grundland, Briot C, Byrd P, Conte R, do Carmo M P, Grundland A M, Grundland A M, Grundland A M, Helgason S, Landau L D, S Post, Winternitz P   +11 more
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Sharp well-posedness for the cubic NLS and mKdV in $H^s({{\mathbb {R}}})$

Forum of Mathematics, Pi
We prove that the cubic nonlinear Schrödinger equation (both focusing and defocusing) is globally well-posed in $H^s({{\mathbb {R}}})$ for any regularity $s>-\frac 12$ .
Benjamin Harrop-Griffiths, Rowan Killip, Monica Vişan   +2 more
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Theoretical analysis of a water wave model with a nonlocal viscous dispersive term using the diffusive approach

Advances in Nonlinear Analysis, 2017
In this paper, we study the following water wave model with a nonlocal viscous term:
Goubet Olivier, Manoubi Imen
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A 3-component extension of the Camassa-Holm hierarchy

, 2006
We introduce a bi-Hamiltonian hierarchy on the loop-algebra of sl(2) endowed with a suitable Poisson pair. It gives rise to the usual CH hierarchy by means of a bi-Hamiltonian reduction, and its first nontrivial flow provides a 3-component extension of ...
B. Fuchssteiner, B. Khesin, E.G. Reyes, G. Falqui, H. McKean, J.E. Marsden, L.A. Dickey, Laura Fontanelli, M. Pedroni, Marco Pedroni, P. Casati, P. Casati, P. Casati, P. Libermann, P. Lorenzoni, Paolo Lorenzoni, R. Beals, R. Beals, R. Camassa, S. Abenda, S. Liu, V.E. Zakharov, V.G. Drinfeld   +22 more
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